The problem is to multiply $1 \frac{1}{2} \times 3 \frac{1}{2}$ and express the answer as a mixed number in simplest form.

Step-by-step solution:

1. Convert the mixed numbers into improper fractions:

   • $1 \frac{1}{2} = \frac{3}{2}$
   • $3 \frac{1}{2} = \frac{7}{2}$

2. Multiply the fractions: $\frac{3}{2} \times \frac{7}{2} = \frac{3 \cdot 7}{2 \cdot 2} = \frac{21}{4}$

3. Convert the improper fraction into a mixed number: Divide the numerator by the denominator: $21 \div 4 = 5 \text{ remainder } 1$ So, $\frac{21}{4} = 5 \frac{1}{4}$.

Final Answer:

The product is $5 \frac{1}{4}$.

Would you like more details or have any questions?

Here are five related questions to deepen your understanding:

1. How do you convert a mixed number to an improper fraction?
2. What is the general rule for multiplying fractions?
3. How do you simplify fractions after multiplication?
4. How do you convert improper fractions back into mixed numbers?
5. What are some examples of real-life problems involving multiplication of mixed numbers?

Tip: Always simplify fractions to their lowest terms before or after multiplying to avoid extra steps later.